Godel’s incompleteness theorem is not only accepted mathematics, but the first theorem to be subjected to formal proof by means of a computer. The theorem says that maybe 2 + 2 is not always 4, which is hard for many mathematicians to swallow (google “Is Arithmetic Consistent?”), and the reason arithmetic may contain some contradictions is the axiom of extension, the method of proof used to demonstrate that the finite case implies all cases.
If we have assumptions that produce no contradictions, then those assumptions will never describe all of mathematics; if our assumptions describe all that is known in mathematics, then there are contradictions that can be derived from our assumptions.
Gautama the Buddha was very careful about how far the logic he developed could be applied, and in some cases he said things like “(statement such-and-such) goes too far”, meaning that what someone was asking could not be discussed within the logic he had developed to describe his experience.
It’s possible to make very powerful statements about relationships that underlie much of the natural world with mathematics, but it’s not possible to describe the whole of what we know without contradiction. If we can limit ourselves to assumptions that don’t give rise to contradictions, maybe we like Gautama the Buddha can describe our experience in the practice of zazen in ways that communicate something of the relationships involved.
I’ll start: calming of the activity of the mind in the movement of breath, like relaxation of the activity of the body in the movement of breath, is conducive to the induction of a hynogogic state that actually sharpens the wits.
I have to be careful in my assumptions: I can relax, and I can calm down, and I believe science has a lot to offer in this regard, but the attainment of a hypnogogic state will always be “something other than” what I think it to be (as Gautama put it).
That’s why Shunryu Suzuki said that “zazen sits zazen”.
I can drop body and mind, but I can’t attain enlightenment. At a certain point, relaxing is the induction of a hypnogogic state; practice is enlightenment.
When scores of monks a day took the knife because of “the meditation on the unlovely” which Gautama had taught, Gautama gathered the monks and related his own practice before and after enlightenment, which was “the intent concentration on in-breaths and out-breaths”. This, he said, was a thing that was peaceful and conducive to happiness, in and of itself.
The only actions that are included in “the intent concentration on in-breaths and out-breaths” are relaxing the activity of the body with the in-breath and out-breath, and calming and composing the activity of mind with the in-breath and out-breath. The practice begins with awareness of the in-breath and out-breath, and I would argue the rest follows naturally as the body is relaxed and the mind is calmed down.